Problem: Rewrite as a simplified fraction. ${0.37\overline{2} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 372.2222...\\ 100x &= 37.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 335}$ ${x = \dfrac{335}{900}} $ ${x = \dfrac{67}{180}} $